Sequential maximum likelihood estimation for reflected Ornstein–Uhlenbeck processes

Lee, Chihoon; Bishwal, Jaya P. N.; Lee, Myung Hee

doi:10.1016/j.jspi.2011.12.002

Cited by 30 publications

(15 citation statements)

References 15 publications

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“…See, for example, Lee et al [7] proposed a sequential maximum likelihood estimation of the unknown drift of the reflected Ornstein-Uhlenbeck process without jumps; some others are concerned with the problem of statistical parameter estimation for reflected fractional Brownian motion (cf. Hu and Lee [3]; Lee and Song [8]).…”

Section: Discussionmentioning

confidence: 99%

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Asymptotic behavior of parametric estimation for a class of nonlinear diffusion process

Zhu¹

2018

J. Nonlinear Sci. Appl.

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In this paper, a stochastic process, which is a class of nonhomogeneous diffusion process from the perspective of the corresponding nonlinear stochastic differential equation is studied. The parameter included in the drift term are estimated by sequential maximum likelihood methodology. The sequential estimators are proved to be closed, unbiased, strongly consistent, normally distributed, and optimal in the mean square sense.

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Section: Discussionmentioning

confidence: 99%

“…His plan is to observe the process until the observed Fisher information exceeds a predetermined level of precision. Many others focused on the extension to other fields, for example, Lee et al [7], Bo and Yang [2], Kuang and Xie [5] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic behavior of parametric estimation for a class of nonlinear diffusion process

Zhu¹

2018

J. Nonlinear Sci. Appl.

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“…On the other hand, some future work may investigate the other estimators for the other reflected diffusions. For example, Lee et al [22] proposed a sequential maximum likelihood estimation (SMLE) of the unknown drift of the ROU process without jumps; the reflected jump-diffusion or Lévy processes have been extensively investigated in the literature (see [1, 2, 4-6, 10, 12, 14, 32]). …”

Section: Discussionmentioning

confidence: 99%

Parameter estimation for generalized diffusion processes with reflected boundary

Zang

Zhang

2016

Sci. China Math.

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Reflected Ornstein-Uhlenbeck process is a process that returns continuously and immediately to the interior of the state space when it attains a certain boundary. It is an extended model of the traditional Ornstein-Uhlenbeck process being extensively used in finance as a one-factor short-term interest rate model. In this paper, under certain constraints, we are concerned with the problem of estimating the unknown parameter in the reflected Ornstein-Uhlenbeck processes with the general drift coefficient. The methodology of estimation is built upon the maximum likelihood approach and the method of stochastic integration. The strong consistency and asymptotic normality of estimator are derived. As a by-product of the use, we also establish Girsanov's theorem of our model in this paper.

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“…As a remedy for this, a sequential estimation plan (τ (h), α τ (h) ) was proposed in [21]. It is assumed in [21] that the parameter ranges the whole real line α ∈ (−∞, ∞) (i.e., it covers ergodic, non-ergodic, non-stationary cases) and the process {X t } is observed until the observed Fisher information of the process exceeds a predetermined level of precision h (see also [8]). More precisely, {X t } is observed over the random time interval [0, τ (h)] where the stopping time τ (h) is defined as…”

Section: Introductionmentioning

confidence: 99%

On drift parameter estimation for reflected fractional Ornstein–Uhlenbeck processes

Lee

Song

2016

Stochastics

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We consider a reflected Ornstein-Uhlenbeck process X driven by a fractional Brownian motion with Hurst parameter H ∈ (0, 1 2 ) ∪ ( 1 2 , 1). Our goal is to estimate an unknown drift parameter α ∈ (−∞, ∞) on the basis of continuous observation of the state process. We establish Girsanov theorem for the process X, derive the standard maximum likelihood estimator of the drift parameter α, and prove its strong consistency and asymptotic normality. As an improved estimator, we obtain the explicit formulas for the sequential maximum likelihood estimator and its mean squared error by assuming the process is observed until a certain information reaches a specified precision level. The estimator is shown to be unbiased, uniformly normally distributed, and efficient in the mean square error sense.

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Sequential maximum likelihood estimation for reflected Ornstein–Uhlenbeck processes

Cited by 30 publications

References 15 publications

Asymptotic behavior of parametric estimation for a class of nonlinear diffusion process

Asymptotic behavior of parametric estimation for a class of nonlinear diffusion process

Parameter estimation for generalized diffusion processes with reflected boundary

On drift parameter estimation for reflected fractional Ornstein–Uhlenbeck processes

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